Integral of x+2y dx

The solution

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       2            
 -4 + y             
    /               
   |                
   |    (x + 2*y) dx
   |                
  /                 
  5

$$\int\limits_{5}^{y^{2} - 4} \left(x + 2 y\right)\, dx$$

Integral(x + 2*y, (x, 5, -4 + y^2))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 2 y\, dx = 2 x y$
The result is: $\frac{x^{2}}{2} + 2 x y$
Now simplify:

$\frac{x \left(x + 4 y\right)}{2}$
Add the constant of integration:

$\frac{x \left(x + 4 y\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x + 4 y\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                    2        
 |                    x         
 | (x + 2*y) dx = C + -- + 2*x*y
 |                    2         
/

$$\int \left(x + 2 y\right)\, dx = C + \frac{x^{2}}{2} + 2 x y$$

Simplify

The answer [src]

                2                       
       /      2\                        
  25   \-4 + y /               /      2\
- -- + ---------- - 10*y + 2*y*\-4 + y /
  2        2

$$2 y \left(y^{2} - 4\right) - 10 y + \frac{\left(y^{2} - 4\right)^{2}}{2} - \frac{25}{2}$$

                2                       
       /      2\                        
  25   \-4 + y /               /      2\
- -- + ---------- - 10*y + 2*y*\-4 + y /
  2        2

$$2 y \left(y^{2} - 4\right) - 10 y + \frac{\left(y^{2} - 4\right)^{2}}{2} - \frac{25}{2}$$

-25/2 + (-4 + y^2)^2/2 - 10*y + 2*y*(-4 + y^2)

Use the examples entering the upper and lower limits of integration.

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Integral of x+2y dx

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